Estimate to Check Reasonableness in Fraction Word Problems

Students use benchmark fractions (0, 1/2, 1) and number sense to estimate the sum or difference before solving, then compare their exact answer to the estimate to verify reasonableness.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Grade 5 · Fraction Addition and Subtraction Word Problems · question 1 of 3

0 of 20

20 rungs. A star at the top.

Ana pours 1/6 cup of juice, then 2/6 cup more. About how many cups of juice is that, to the nearest half cup?

How it is taught

0:00 of 3:26

An estimate is a nearby amount you use to check an answer.

You round each fraction to 0, half, or 1 before you add.

A reasonable answer sits close to that estimate.

Read it: Is the answer about right?

7/8 + 2/5: 7/8 is close to 1, and 2/5 is close to 1/2. So 7/8 + 2/5 is about 1 + 1/2, which is 1 1/2.

Put each fraction on a number line and find its nearest benchmark: 0, 1/2 or 1.
Hop each fraction to that benchmark.
Add or take away the benchmarks: that is the estimate.

Benchmarks are numbers you can add in your head, so the estimate is quick.

A fraction near its benchmark changes the answer only a little, so the estimate stays close to the exact answer.

An estimate checks an exact answer: 7/8 + 2/5 cannot be 9/13, which is less than 7/8 alone.

Round each fraction to its nearest benchmark, then add or subtract the benchmarks to estimate.

Adding the tops and the bottoms: 7/8 + 2/5 = 9/13, which is about 1/2.

9/13 is less than 7/8 alone, so it cannot be the sum. The benchmarks say about 1 1/2.

About how much is 8/9 + 11/12? — 2. 8/9 is close to 1 and 11/12 is close to 1: 1 + 1 = 2.

7/8 + 1/9

Maya ate seven-eighths of a pizza. Her little brother ate one-ninth. About how much pizza did they eat together?

Before we solve, let's estimate using our benchmark fractions: zero, one-half, and one.

Seven-eighths is very close to one whole — almost the entire pizza.

One-ninth is tiny — much closer to zero than to one-half.

So our estimate is about one plus zero, which is about one whole pizza.

Now let's find the exact answer. We need a common denominator for eight and nine.

Eight times nine is seventy-two. Rewrite each fraction with seventy-two on the bottom.

Sixty-three plus eight is seventy-one. So the exact answer is seventy-one seventy-seconds.

Seventy-one seventy-seconds is just one piece away from seventy-two seventy-seconds — almost one whole.

Grade 5 · Use benchmarks 0, 1/2, 1 to check your answer

Our estimate said about one, and the exact answer is almost one. That matches — our answer is reasonable!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free